Papers

We study charge transport in a magnetized relativistic plasma using kinetic theory within the relaxation-time approximation. By exactly solving the linearized Boltzmann equation in a uniform magnetic field, we obtain an analytic solution for the distribution function in terms of Bessel functions. Using this solution, we compute the full set of retarded current-current correlators and verify the Ward identities. In the hydrodynamic limit, we extract the charge diffusion modes, demonstrating that the transverse diffusion coefficient is strongly suppressed by the magnetic field, scaling as $1/B_0^2$ in the strong-field regime, while the longitudinal diffusion remains unaffected. Furthermore, we analyze the non-hydrodynamic branch cuts in the complex frequency plane, determining their kinematic thresholds and identifying the underlying wave-particle interactions as longitudinal Landau damping and transverse cyclotron damping.

Weyl conformal geometry is the natural underlying geometry of gauge theories of Weyl group (of dilatations and Poincaré symmetry), such as Weyl quadratic gravity and its generalisation, Weyl-Dirac-Born-Infeld action (WDBI). These are local, Weyl-anomaly free (quantum) gauge theories of gravity. We describe Weyl gauge symmetry from a more familiar Riemannian view of Weyl gauge invariant dressed fields by the Wilson line of dilatations. Weyl geometry can then be seen as Riemannian geometry of non-local dressed metric ($g_{\mu\nu}^*$), at the "cost" of (gauge-induced) non-commutativity in the UV, due to Wilson line. Then Weyl quadratic gravity and WDBI actions of Weyl geometry, which are Weyl gauge invariant in $d$ dimensions, have the same expression in Riemannian geometry defined by $g^*_{\mu\nu}$. This is a non-local map and dual description of the two geometries and actions in the symmetric phase. Unlike for the metric, the equation of motion of Weyl gauge field ($\omega_\mu$) does not commute with the dressing of the metric. Quantum non-locality, in particular entanglement, and non-commutativity are (gauge-invariant) physical artefacts of "translating" (local) Weyl geometry and Weyl gauge covariance into our real-world Riemannian geometry of Weyl gauge invariant observables, and they are evidence of Weyl gauge symmetry. At lower energies, $\omega_\mu$ becomes massive, can decouple and Einstein-Hilbert action and commutativity are recovered. The case of a light $\omega_\mu$ is also discussed.

We study a disorder-free variant of the Sachdev-Ye-Kitaev (SYK) model with dissipation within the Gorini-Kossakowski-Sudarshan-Lindblad formalism. By utilizing the integrability of the clean SYK model, we derive an exact solution in a spectrum-resolved form, i.e., the eigenvalues and corresponding projection superoperators of the Liouvillian for arbitrary system size $N$. We determine the scaling of the gap that governs the long-time decay of the two-point correlation functions. Importantly, the gap does not vanish in the dissipationless limit when the thermodynamic limit is taken first, despite the integrability of the model. This phenomenon, known as anomalous relaxation, suggests a possible connection with chaotic dynamics and quantum Ruelle-Pollicott resonances. We also find several spectral features, such as transitions in the Liouvillian spectrum from complex to real eigenvalues with increasing dissipation strength, as well as the convergence of the dissipative form factor to the spectral form factor in the dissipationless limit. These findings indicate that the present model offers a useful platform for exploring nontrivial open dynamics of many-body quantum systems.

The smeared null energy condition (SNEC) imposes a semilocal bound on the negative energy accumulated along null geodesics. In eternal inflation, rare stochastic upward fluctuations of the inflaton locally increase the Hubble parameter, creating an apparent tension with the SNEC. Focusing on a canonical single-field model, we investigate whether this quantum-induced self-reproduction violates the SNEC. Using the Fokker-Planck equation, we demonstrate that the ensemble drift of the Hubble parameter is parametrically bounded by slow-roll parameters and semiclassical suppression. Furthermore, a complementary single-trajectory analysis reveals a strong timescale hierarchy, $N_{\rm SNEC} \gg N_{\rm BR}$. This indicates that even for rare upward stochastic excursions, gravitational backreaction invalidates the background spacetime assumption long before the SNEC bound can be mathematically approached. We conclude that while standard stochastic diffusion drives eternal inflation, it does not inherently lead to SNEC violations within the semiclassical slow-roll regime.

We develop a self-consistent dressing for $(1+1)$d Dirac fermions with Fierz-complete four-fermion interactions, extending the spin-charge formalism of~\cite{Haddad2024}. By studying the associated composite connection, we characterize obstructions to trivializing the Dirac operator and prove a trivialization theorem under which spin-charge separation, half-infinite Wilson-line dressing, and flat-connection holonomy arise as regime limits of the single dressing. In particular, the chiral-difermion transition is a deconfinement transition for the spin and charge degrees of freedom, mediated by an emergent $\mathfrak{sl}(2,\mathbb{R})$ gauge field and measured by a Wilson-loop area law in the chiral phase. We show that our formulation provides a realization of the conjectured Faddeev–Niemi link between spin-charge separation and confinement.

The Renormalization Group flow connects microscopic to macroscopic descriptions of a system and is therefore typically considered as an initial-value problem. Motivated by situations in which different couplings within a system of Renormalization Group equations are constrained at different scales, we instead consider boundary-value problems in Renormalization Group flows. We find that, unlike initial-value problems which provide $n$ conditions for $n$ couplings, boundary-value problems which provide $n$ conditions for $n$ couplings do not always have a unique solution. When the Jacobian matrix, i.e., the matrix of first derivatives of beta functions, has complex eigenvalues, boundary-value problems may be non-unique. We provide a diagnostic tool for non-uniqueness in systems with many couplings. We also provide two examples with potential relevance for physics, namely within the Standard Model as well as within the Einstein-Hilbert truncation of asymptotically safe quantum gravity.

Public-key cryptosystems eliminate the requirement for pre-shared secret keys by enabling encryption with a publicly disclosed key and decryption with a corresponding private key. In this article we generalize the public-key cryptosystems to ternary algebraic structures, with particular attention to ElGamal as a representative family. We introduce the necessary algebraic background for nonderived ternary structures, including special elements, ternary group rings, and a matrix ternarization procedure that maps binary rings and group rings to antidiagonal symbolic matrices closed under ternary multiplication. Building on these foundations, we formulate a ternary analogue of the ElGamal three-step protocol (key generation, ephemeral encryption, and decryption via querelements) and derive explicit ternary power and querelement formulas that enable correct decryption. Concrete instantiations and numerical examples over a ternary fraction field, a matrix-ternarized finite group ring, and a finite \((6,3)\)-ring (field) validate the construction and illustrate admissible word-length quantization and cycle behaviour of ternary powers. The ternary framework highlights two practical advantages: richer algebraic structure (querelements replace binary inverses) that increases algebraic complexity for attackers, and higher information density (matrix ternarization transfers paired/plaintext vectors). Formal hardness assumptions, optimized parameter choices, and comprehensive security and performance analyses remain necessary future work.

Magnetic Skyrmions are planar solitons stabilized by the Dzyaloshinskii-Moriya interaction (DMI) and realized in chiral magnets. We study their natural three-dimensional generalization: a sigma model from $\mathbb{R}^3$ to $S^3$ with a four-component magnetization vector, stabilized by a one-derivative term which is a generalized DMI. We utilize two SO(3)-invariant generalized DMIs discovered recently: an "$\alpha$-term" supporting a spherically symmetric hedgehog Skyrmion and a "$\beta$-term" supporting an axially symmetric Skyrmion that splits into two half-Skyrmions connected by a magnetic string of negative tension, a phenomenon we call "anti-confinement". We derive a cubic-lattice discretization that reproduces both continuum theories at long wavelengths and use Monte Carlo simulations to map the finite-temperature phase diagram. We identify spin-spiral, magnetic-string-lattice, Skyrmion-lattice, and antiSkyrmion-lattice phases, as well as a mixed-topology regime with fractional $S^3$ charges localized at string bends. We find, for the first time in the literature to the best of our knowledge, a toroidal (anti-)soliton of unit charge. Our results establish a theoretical and computational framework for three-dimensional topological magnetic textures in systems whose order-parameter manifold is $S^3$.

Wilson lines are fundamental probes of gauge theories. We show that, in sufficiently rich representations, they support a large new class of operator insertions. For half-BPS lines in $\mathcal{N}=4$ SYM, some have the quantum numbers of the displacement supermultiplet and define natural defect deformations. By relating their beta-functions to chiral ring OPE coefficients, we show that these deformations are marginally irrelevant, meaning the half-BPS line is IR stable for all representations. We connect these deformations to multidimensional RG flows and find evidence for new conformal line defects.

We provide a complete classification of twisting supercharges for type IIA supergravity in a flat background by determining the orbits of square-zero elements in the $\mathcal{N}=(1,1)$ super Poincaré algebra in ten dimensions under the action of the Spin group. Together with recent results for type IIB, this completes the description of the moduli space of twists for type II supergravities. We show that the type IIA nilpotence variety is the union of the eleven-dimensional nilpotence variety and a second component, confirming a conjecture of Eager, Saberi, and Walcher, and determine which twists of type IIA arise via dimensional reduction. Using the pure spinor formulation of the superstring, we construct maps from the moduli spaces of worldsheet twists to those of target space twists for both type IIA and type IIB, and find that these maps are not surjective. Precisely those twists of supergravity whose stabilizers are special holonomy groups—$G_2$ in type IIA, $\mathrm{Spin}(7)$ and $\mathrm{Sp}(4)$ in type IIB—have no corresponding background on the pure spinor worldsheet. Finally, we work out the action of T-duality relating twists of type IIA and type IIB, and find an obstruction to dualizing the $G_2$-twist of type IIA along certain directions.

Motivated in part by anomaly cancellation for integral charge spectra in chiral gauge theory, we study the symmetric locus in the ideal degree-three Prouhet-Tarry-Escott problem. A symmetric integer solution is one whose entries are paired about a common center $c\in \frac12\mathbb Z$. This symmetry reduces the problem to a sum-of-two-squares equation, $x^2+y^2=u^2+v^2$, in integer variables, subject to the appropriate parity conditions. Thus the problem is governed by representations as sums of two squares. For the full symmetric locus, let $N_{\mathrm{sym}}(H)$ denote the number of nontrivial symmetric integer solutions of height at most $H$, counted with unordered multiset conventions and summed over the admissible centers. Then \begin{align*} N_{\mathrm{sym}}(H) = \frac{4\log 2}{3\pi^2}H^3\log H+O(H^3). \end{align*} The logarithmic enhancement comes from the second moment of the sum-of-two-squares representation function. In particular, the symmetric locus is larger than one would expect from the naive $H^3$ degree-weighted box-counting scale alone. This asymptotic identifies a large arithmetically structured subfamily of the ideal degree-three solution space, and suggests that paired anomaly-free integral charge spectra reflect a fundamental number-theoretic structure.

We extend the study of boundary criticality in the Gross-Neveu-Yukawa universality class beyond leading order. Using the hyperbolic space formulation of boundary conformal field theories, we compute the first subleading corrections at large $N$ to the free energies of the “normal", “ordinary" and “special" boundary universality classes. We also determine the order $1/N$ correction to the dimension of the boundary fermion at the normal fixed point. In the Gross-Neveu-Yukawa theory in $d=4-\epsilon$, we perform a higher-order analysis of the boundary free energy, and use it to extract estimates for the boundary central charge in $d=3$. The large $N$ and $\epsilon$-expansion results are shown to be precisely consistent in overlapping regimes, providing nontrivial consistency checks for the identification of the boundary universality classes. Our calculations rely on a combination of AdS harmonic analysis and boundary conformal field theory techniques.

In this paper, the large N behavior of a supersymmetric matrix model is compared with its exact continuum description. We concentrate on the large N limit of a supersymmetric matrix model describing a supermembrane with central charge on a toroidally compactified target space. We analyze, on the one hand, the supermembrane model formulated on a differentiable compact torus without boundary, with structure group given by the area-preserving diffeomorphisms, and, on the other hand, the associated regularized $SU(N)$ model. We emphasize in our analysis the structure of the constraints of the regularized model, which generate the $SU(N)$ algebra and reproduce the area-preserving diffeomorphism algebra in the large N limit, together with the topological information associated with the central charge of the model. We explain the role of the central charge in the compactified supermembrane and how it allows a top-down $SU(N)$ regularization. It is known that the regularized model has discrete spectrum. We prove, in the semiclassical approximation of the models, that in the large N limit the eigenvalues of the Hamiltonian of the supersymmetric matrix model are in one to one correspondence with, and converge exactly to, the eigenvalues of the Hamiltonian of the supermembrane (M2-brane) with central charge. Finally, we discuss some physical consequences of this result.

During cosmological inflation, inhomogeneities arising from quantum vacuum fluctuations are stretched to become super-Hubble and effectively classical. As many scenarios of the origin involve nonlinearities or a breakdown of perturbativity in the infrared, the limitations of quantum field theory can be addressed using a stochastic description of the dynamics, the so-called stochastic inflation paradigm. However, the stochastic formalism was only recently formulated consistently within full General Relativity and has not yet been extended to more general theories of the early universe, which is the subject of this work. In order to find the stochastic sources for a wide class of fully nonlinear scalar-tensor theories, we apply our gauge-agnostic coarse-graining procedure to the linear equations of the associated effective field theory. Each theory can then be mapped to its own set of stochastic equations of motion by identifying the corresponding coefficients in the former. We illustrate this with a few concrete and, in most cases, unprecedented examples, including Gauss-Bonnet, generalized Brans-Dicke, Horndeski, and braiding theories. Finally, we discuss other natural extensions to provide a phenomenologically complete stochastic framework. For example, we showcase the coarse-graining of multifield inflation in full General Relativity and argue for the generality of our procedure and thus its potential applications beyond the realm of inflation.

We consider double Wick rotation in field theories, which analytically continues the time coordinate, and then reinterprets one of the spatial directions as the new Lorentzian time. We show that if Lorentz-invariance is absent, Wick-connected theories are no longer necessarily equivalent. Focusing on flat spacetime, we study the propagating modes, unitarity and renormalizability of such Wick-connected theories, and provide criteria for when such notions fail to translate.

In a recent paper, Arxiv:2605.23077, we have demonstrated that (conformal) Killing vectors give rise to stealth vector solutions of a specific bumblebee-type Proca theory supplemented by fine tuned curvature terms. Here we show that such a construction readily generalizes to hidden symmetries encoded in (conformal) Killing-Yano tensors, giving rise to the corresponding p-form stealth solutions. Similar to what happens with Killing vectors, the construction works on any background, providing a "physical visualization" of its symmetries. Several examples of spacetimes with so constructed p-form stealth hair are presented.

Several studies of black hole ringdown from particles plunging into black holes have identified contributions decaying at integer multiples of the surface gravity, called redshift modes, horizon modes, and direct waves. We show that, for Schwarzschild black holes, every one of these contributions has vanishing amplitude in the observable waveform. The cancellation follows from causality, which forces the source-integrated Green function to vanish on the light cone. Individual quasi-normal mode overtones still carry non-zero redshift-mode contributions, but these cancel exactly once the sum over overtones is performed; the so-called impulsive contribution to the waveform acts precisely as the counterterm enforcing this cancellation. Finally, we provide a motivation to the standard regularization of quasinormal mode excitation coefficients since divergences give rise to vanishing redshift modes.

We study the emission of gravitational waves by a test particle orbiting a non-rotating black hole in higher-derivative gravity theories with cubic and quartic contractions of the Riemann tensor. To this aim, we first derive the master equations describing even- and odd-parity perturbations in the presence of an arbitrary source term, and then construct a Post-Minkowskian expansion of the solutions to the homogeneous master equations. Specializing to a circular binary system, we compute the Post-Newtonian expansion of the waveform, as well as the energy and angular-momentum fluxes at infinity. We show that higher-derivative corrections to the waveform and to the fluxes always appear at 5PN order, and are universally proportional to the Love number describing the deformability of the geometry under the $\ell=2$ mode perturbation. These analytical results are validated against numerical computations, which also allow us to extend the analysis to larger velocities.

We study quantum anomalies associated with $U(1)$ 1-form symmetries from the perspective of invertible phases and bordism. We compute the oriented and spin bordism groups of the Eilenberg-Mac Lane space $K(\mathbb{Z},3)$ up to degree 8 using the Atiyah-Hirzebruch spectral sequence, resolving the relevant extension problems by geometric arguments and identifying both bordism invariants and geometric generators. We then relate these invariants to perturbative and global anomalies, and discuss physical examples and top-down constructions of the corresponding anomaly terms. For 5-dimensional theories, we find a new mixed perturbative anomaly between the $U(1)$ 1-form symmetry and spacetime diffeomorphisms, while for 7-dimensional theories we find a new $\mathbb{Z}_2$-valued discrete anomaly intrinsic to the $U(1)$ 1-form symmetry. We also discuss their boundary realizations and give new physical interpretations of these anomalies.

We consider two sets of related models: initially, these are $SU(2)$ antiferromagnetic spin chains with $N$ sites of spin $S$, and the $O(3)$ nonlinear sigma model in two dimensions with topological coefficient $\Theta$ a multiple of $\pi$ (and later, the extensions of these with any semisimple Lie group symmetry). It is known that, in a continuum description, the low-energy behavior of the spin chain is given by the sigma model with $\Theta=2\pi S$. We study these models with $N$ odd and with antiperiodic (A) boundary condition (b.c.), respectively, which correspond. The A b.c. in the sigma model involves the $\mathbb{Z}_2$ inversion symmetry $\vec{n}\to-\vec{n}$, and amounts to a flux of a $\mathbb{Z}_2$ gauge field through a spacetime torus; summing over the two b.c.s for each direction would amount to gauging the $\mathbb{Z}_2$ inversion symmetry. We show directly that, if and only if $(-1)^{\Theta/\pi}=-1$, the gauging cannot be carried out; there is an 't Hooft anomaly. The partition function for the A b.c. exists, but is not gauge invariant; consequently, the sum over b.c.s cannot be made modular invariant. The gauged model would be a sigma model with target space $\mathbb{R}\mathbb{P}^2\cong \mathbb{S}^2/\mathbb{Z}_2$, and hence this model does not exist for $\Theta=\pi$ (mod $2\pi$). A related result is that, using semiclassical quantization, in the spin chain we obtain the known values of the ground-state crystal momentum, which at leading order depend only on $N$ modulo $4$ and $2S$ modulo $2$. For a large class of spin chains and associated sigma models we find similar results, but now $(-1)^{\Theta/\pi}$ is replaced by the value $\pm 1$ of the square of the time-reversal operator acting on a single spin, which is still determined by the coefficients of the topological terms, in a way that depends on the symmetry group.

The weak cosmic censorship conjecture (\WCCC) and the weak gravity conjecture (\WGC) sit at the heart of how singularities and charged matter are constrained in any consistent theory of quantum gravity. We study both conjectures for Einstein–Maxwell–power–Yang–Mills–AdS (\EMPYM) black holes, a family in which a non-Abelian power-law Yang–Mills field, a Maxwell field, and a negative cosmological constant act together. Working in holographic conformal field theory (CFT) thermodynamics, we treat the central charge $C$ and the CFT volume $\Vol$ as independent variables and obtain an extended first law that carries variations of the Yang–Mills charge and of the nonlinearity exponent $\gamma$. A closed Euler relation follows, and we check it together with the full set of equations of state to machine precision. The perturbation is a charged massive scalar minimally coupled to the Maxwell sector. Its horizon energy and charge fluxes fix the superradiance threshold $\omega<\tilde{q}_s\tilde{\phi}_h$, and the mass–energy relation $\mu_s=\omega$ turns this into the bound $\tilde{q}_s/\mu_s>r_{\min}/\tilde{Q}$. Expanding the metric function $f(r)$ about its minimum for extremal and near-extremal configurations, we find that absorption keeps $f_{\min}$ non-positive, so the horizon survives. The Yang–Mills sector lowers the effective charge-to-mass threshold below the Reissner–Nordström value of unity, while a local stability analysis locates a Davies point in the heat capacity. Across the parameter range examined the \EMPYM\ family respects cosmic censorship under scalar perturbations, with the \WGC\ fixing only the direction of evolution toward or away from extremality.

We settle the projectedness problem for the compactified unpunctured supermoduli stack in every genus at least two. In genus two, the odd component is split, whereas the even component is non-projected. In every genus $g\geq 3$, both compactified parity components are non-projected.

The confining flux tube of $(3+1)$d QCD is described by an effective string theory with $(1+1)$d worldsheet action that extends the Nambu-Goto form by the addition of a massive pseudoscalar worldsheet “axion". As argued in companion papers concerning the modified phenomenology of the Lund string model at colliders, QCD flux tubes produced by high-energy collisions are likely to involve excitation of both worldsheet Nambu-Goldstone and axion modes, although the standard Lund model assumes a constant tension ground-state string. Here we detail the path-integral computation of the modified Schwinger-like process of string breaking via nucleation of quark-antiquark pairs in the presence of excitations above the string ground state. We find that the worldsheet axion leads to the dominant change in the string breaking process, the axion excitations producing, among other effects, a varying effective tension of the string, which can exponentially enhance or suppress the string breaking rate depending on the local phase of the excitation. Our computation employs a version of the Schwinger-Keldysh complex time contour method with initial state data specified by a density matrix. In an excited background the Euclidean saddle point is generically complex, but its continuation gives real initial data for post-decay evolution. Our results are of relevance for hadronisation models with excited QCD strings.

In AdS/CFT at finite N, black holes are described by ordinary quantum systems with finite entropy and discrete spectra, while semiclassical bulk effective field theory treats the near-horizon region as an ideal continuum. We reconsider the brick-wall model as a simple effective description of the finite N departure from the semiclassical near-horizon continuum in AdS/CFT. A Dirichlet wall is reflecting; however, once the regulated near-wall modes are replaced by interacting stretched-horizon degrees of freedom, the exterior simple sector can look absorptive and black-hole-like. If these degrees of freedom are thermally populated while the exterior incoming modes are in their vacuum, they radiate as an ordinary hot object, and this gives Hawking radiation. Furthermore, we show that finite N prevents the near-horizon sector from being an ideal continuum absorber; the brick-wall model is a simple effective representation of this limitation, where the failure of perfect absorption appears as residual reflection or echoes. Such return effects will not be suppressed as $e^{-S_{\rm BH}}$, although their detailed amplitude is model-dependent. We also discuss brick-wall-like models in which the effective inner boundary arises dynamically from a regular matter core rather than from an imposed boundary condition.

We investigate the LHC phenomenology of a vector dark-sector effective theory containing two neutral massive vector states, both odd under a dark-parity symmetry. The lightest state is stable and provides a dark-matter candidate, while the leading interactions with the Standard Model arise from dimension-six operators involving the hypercharge field strength. In the prompt-decay regime considered in this work, the heavier state can decay radiatively, leading to a $\gamma+\text{jets}+E_T^{\text{miss}}$ signature when the two dark vectors are produced in association with QCD radiation. We study this topology at the LHC through a cut-based analysis, comparing an inclusive missing-transverse-momentum selection with a three-bin strategy that retains coarse shape information. The binned analysis is found to substantially improve the expected reach and probes regions of the parameter space compatible with the observed relic abundance in the standard freeze-out scenario. We also discuss the freeze-in interpretation and the limitations associated with the EFT description at high masses.

We study one-point functions of composites of charge $e$ operators in the presence of a monodromy defect for a $U(1)$ global symmetry with monodromy $\beta$. We first compute these in free massless and massive theories, recovering in the former case the known $\sin(e\pi\beta)$ dependence and obtaining in the latter a $\sin^2(e\pi\beta)$ dependence. We then turn to holography and compute 1-point functions for operators $O$ of charge $J=\Delta$ in $\mathfrak{su}(N)$ $\mathcal{N}=4$ SYM in the presence of a monodromy defect for a $U(1)\in SO(6)_R$. From a WKB analysis in large $\Delta$ we recover the structure of standard and anchored saddles previously found in the literature, finding that, to subleading order in $1/\Delta$, the anchored regime is resolved by a boundary layer effect. Finally, using heat kernel methods, we determine the monodromy dependence of the induced 1-point function for the composite $O^{\dagger}O$, finding a smooth $\sin^2(J\pi\beta)$ behavior.

We compute the disk one-point function, the disk two-point function, and the annulus one-point function of the cosmological constant operator in the type 0A and type 0B minimal superstring theories with (1,1) ZZ instanton boundary conditions. The moduli-space integrals appearing in the disk two-point function and the annulus one-point function have divergences associated with open-string-channel degenerations, which must be regulated using open-closed string field theory. The definition of the string field theory interaction vertices requires a choice of locations for the picture-changing operators, which we specify in detail. After carefully taking into account all contributions, including those from vertical integration, we find that the results precisely match the expectations from DDK-KPZ scaling. Our technical results on the detailed construction of interaction vertices are a first step toward understanding the analogous quantities in the ten-dimensional type IIB superstring, where one also needs to understand how to treat the bosonic and fermionic collective coordinates at subleading order.

We compute the one-loop correction to the CFT data of all double-trace operators $[\phi\phi]_{n,\ell}$ for a $\Phi^4$ theory in AdS$_3$, for arbitrary values of $n$, $\ell$, and of the scaling dimension $\Delta_\phi>1$. Working in the spectral representation, the $t$-channel one-loop bubble diagram is reduced to a product of spectral integrals dressed by the conformal $6j$ symbol. Both the spectral integrals and the subsequent sums over residues are performed analytically, yielding finite closed-form expressions for the anomalous dimensions in terms of higher hypergeometric functions. We discuss the structure of the results, including their large-spin and high-energy behaviors, and show that the anomalous dimensions are completely monotonic in spin.

We study inner products and partial amplitudes of graph states–a commonly employed class of quantum states, which are specified by graphs. We find that the magnitudes of these quantities are simply related to the rank of the adjacency matrix of the graph over F_2 while the phase is determined by the Arf invariant of its quadratic refinement. These facts motivate a nonlocal tensor factorization of the Hilbert space, with respect to which all graph states are products of Bell pairs with unentangled ancillae. These results may illuminate the quantum advantage in the framework of Measurement-Based Quantum Computation and suggest that graph states can be usefully visualized in the language of algebraic topology. In addition, we develop a specialized technique for computing expectation values of qubit-wise permutations in graph states, which is useful for calculating multi-invariants.

Lecture notes on inflation. The lectures are three double lectures, held for the first time at the Nordita Winter School 2024 - Particle Physics and Cosmology, covering an advanced introduction to the theory of primordial inflation, as well as the linear and non-linear perturbation theory of slow-roll inflation/quasi-de Sitter spacetimes.